Problem: Simplify the following expression: $p = \dfrac{z^2 - 15z + 50}{z - 5} $
Explanation: First factor the polynomial in the numerator. $ z^2 - 15z + 50 = (z - 5)(z - 10) $ So we can rewrite the expression as: $p = \dfrac{(z - 5)(z - 10)}{z - 5} $ We can divide the numerator and denominator by $(z - 5)$ on condition that $z \neq 5$ Therefore $p = z - 10; z \neq 5$